Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

Ian M. Musson, Georges Pinczon, Rosane Ushirobira

Published 2008-10-01, updated 2009-03-18Version 4

We give a complete study of the Clifford-Weyl algebra ${\mathcal C}(n,2k)$ from Bose-Fermi statistics, including Hochschild cohomology (with coefficients in itself). We show that ${\mathcal C}(n,2k)$ is rigid when $n$ is even or when $k \neq 1$. We find all non-trivial deformations of ${\mathcal C}(2n+1,2)$ and study their representations.